High-frequency resistance



May 7, 1946. K. E. LATIMER HIGH FREQUENCY RES ISTANCE Filed Jan. 8, 1943 'Illll I 1/;///////////I/l/////l/l/Ill/I/l INVENTOR KEV/V57 E. 1477/)? ATTORNEY Patented May 7, 1946 *um'rao' STATES PATENT OFFICE 2,399,: mdn-ranoumcr assrs'raivca ram Eric mum, Ilendon, land, a-ignor to The Hartford 3 m Company, Hartford, Conn,

National m as Application January 8, 1943, Serial No. 471,724

In Great Britain January 9, 1042 9 Claims.

inductance Lo and capacity Cc obey the relation ga' (1) where R is the value of the resistance. It is immaterial whether the effective capacity is considered toshunt the resistance alone, or the resistance and inductance, as both arrangements are imperfect representations of the actual conditions. In general such a plan works well enough for frequencies well below the cut-off oi the half section of low pass filter represented by L0 and Co. except as regards skin eflect which is calculable and can be prevented from having undue influence by the use of suitably thin materm.

If the resistor is composed of a coil of wire, the cut-oil oi the hypothetical filter will generally be quite low. In the most favourable case in which the resistor is ashort element of compara'tively high resistance material, the cut-oil, may be raised to a value at which the dimensions of the resistance element become comparable with a wave-length.

The chief object of the invention is to enable a resistance to be constructed in such a way as to have a constant value (apart from skin effects) up to a frequency such that the wavelength may be considerably shorter than the dimensions of the resistor. Apart, from obvious constructional advantages, this procedure enables a considerable power to be dissipated in the resistor without damage. It will further be. shown that in one embodiment of the invention, the power is dissipated in the resistance element in a uniform manner, which still further raises the allowable dissipation. Another object 01' the inventicn is to enable the terminals of the resistor to be brought out in such 'a way that they are capable of direct connection to a coaxial line of the type used in communication systems.

Let the resistance per unit length of the resistance element be R (where R may possibly be a function or length), then according to the invention the capacity and inductance per unit length of the circuit of which the resistance element forms part-(the meaning of the word circult in this connection will be made clear later),

should be so proportioned that at the point a:

along the length of the resistance element the characteristic impedance Under these circumstances the circuit containing the resistance element will present a constant resistance at its terminals even it the resistance element is several wave-lengths long.

This relationship will now be justified. Suppose that the resistance element is surrounded wholly or partially by a return-circuit in order that both terminals may occur at the same end of the resistance element. A preferred embodiment would be to have the return conductor coaxial with a cylindrical resistance element, but this is not essential. Itis further supposed that the dimensions of the resistance element and return conductor are such that there is no appreciable axial component of electric field, i. e., the structure is to be considered comparatively long compared with its own diameter. In some instances it may be desirable to make the return conductor also a resistance element in which case the return conductor is made of a suitable resistance material.

At the end remote from the terminals. the resistance and the return conductor are short circuited together. Take this short circuit as the origin for x, the distance along the resistance element, and at a given distance 2 consider the increment of impedance added by a length d: of resistance element and return circuit. If the total impedance of the resistance and return conductor at the point x is Z then the impedance at point z+d:c can readily be shown to be neglecting higher order terms.

By the binomial theorem, again neglecting higher order terms 'z+dz=z+ R+ wL- -0z de 4 Now if L: oz or (-==-z (5) Then dZ=Rdx (6) Z =2 (see Equation 2) (7) Fromthisitisreadilyseenthatthetotalimpedance of the element and its return conductor at any frequency will be the ohmic resistance of the element, apart from skin eflect.

A particularly desirable solution occurs when R is constant. In this case Z=Rz (9) In this case the return conductor should be made in the form or a logarithmic horn," in which the throat has the same diameter as, and is connected to, the resistance rod, and the open end has the same internal diameter as that of the outer conductor of a co-axial line to which the resistance is connected. If, however, the outer diameter of the inner conductor of the co-axial line is the same as that of the resistance element, and if the total resistance of the resistance rod, assumed uniform, is equal to the characteristic impedance of the co-axial line, the latter will be smoothly terminated at all frequencies, apart from skin effect. In practice, in order to achieve this, the resistance element may consist of a very thin layer of conducting material applied to the surface of a suitable dielectric, so as to avoid troubles due to skin effect.

The logarithmic relationship arises in the following way. The inductance in electromagnetic units of a coaxial line is 2 log, {5-

In the case of the coaxial line attached to the resistance element the same formulae apply except that 41 becomes D2, the inner diameter of the outer conductor of the co-axial line. Since the impedance of an elemental length is thus proportional to the inductance, in fact Z=VL where V is the velocity of light, all that is necessary to satisfy the relationship Z=Rx is to make where X is the length of the resistance rod; also RX must be made equal to the impedance of the coaxial line.

In the above reasoning it has been assumed that the resistance of the return conductor is negligible, so that in the design either the resistance rod must not be made too long, or the finite resistance of the return conductor must be taken into account.

It will now be shown that in the case of the preferred embodiment the dissipation of energy along the rod is uniform.

The equations for the current flowing in the resistance rod are as follows:

aseaeu ,If i is the current flowing at point a and i that at x+dz then Substituting for C from (5), (9,) and (10),

di=i i= -l dz di 2., are

where in is the current at the shorted end of the resistance rod.

The current is thus constant in magnitude throughout the rod although its phase angle is variable. Hence the heating of therod is uniform considering long time intervals.

By similar reasoning it may be shown that the voltage V to the return conductor at point x is given by 11 V=Rxi e V) a conclusion which may also be reached from (9) and (12).

As a further development the resistance rod may be filled with some fluid having a suitable thermal expansion or alternatively may contain a thermocouple or other means of measuring temperature, in which case the terminating arrangement may serve as a wattmeter to measure the power transmitted along the coaxial line.

The invention will be further described with reference to the appended drawing showing a resistor in accordance with a preferred embodiment of the invention. The resistor there shown comprises a cylindrical core iii of dielectric material such as electrical porcelain, glass, Isolantite or of other ceramic material or may consist of a non-ceramic insulating material such as polystyrene, or the like.

Disposed on the surface of the core II and extending to the ends thereof is a resistance element H consisting of thin layer or coating of electrical resistance material, for example, a sprayed or adhesively-bonded coating of carbon, or a metal coating of tungsten, platinum, or Monel metal forming a metallized coating on the surface of the core 10. Tungsten can be applied by sputtering, platinum by sublimation, sputtering or sintering, while the Monel metal coating can be produced in situ by electrodepositing copper and nickel separately.

Electrical connection to the ends of the resistance element II is obtained by bands I! and I! consisting preferably of a coating or plating of low resistance metal such as silver.

concentrically surrounding the resistance element iii-H is a metal sleeve I4 which in accordance with a preferred embodiment of the invenassaoss I 3 tionhasthe shape cfalogarithmic horn. asuitablematerialforthesleeve llisbrasswhichhas been electrolytically. silver plated and rhodium flashed Anyothermetalwhichcanbeplated ,in alike manner, can be used. In instances 5 wherethesleeveisinitselftoformpartofthe.

resistance element, it may consist of a thin shell of-metal or a molded matrix of carbon suspended in a suitable binder. The throat portion of the sleeve It has an internal diameter only slightly larger than the external diameter of the terminal band I! and is electricall connected to the terminal band by soldering, brazing, or the like.

External electrical connections to the resistor are made in suitable manner to the band I! and centric transmission line, the dimensions of the sleeve II- and the element ll-ll are so chosen that the connecting portions coincide with the outer conductor and the inner conductor respectively of the transmission line.

As above pointed out, the resistor is also suitable for use as a high frequency wattmeter For this purpose the core ll may be filled with a fluid having a suitable thermal expansion, 1. e. monostyrene or benzene, to which is connected a pressure-measuring instrument calibrated in watts; alternatively; there may be positioned within the resistor element, a thermocouple element connected to a voltmeter calibrated in watts.

While I have described my invention by means of specific examples and in a specific embodiment I do not wish to be limited thereto for obvious modifications will occur to those skilled in the art without departing from the spirit and scope of the invention. v

Iclaim:

1. An electrical resistor comprising an insulating core, a resistance element forming a coating on said core, and an electrically conducting sleeve member surrounding the element, said sleeve being in the form of a logarithmic horn having its throat portion connected to one end element.

2. An electrical resistor comprising an insulating core, a resistance element forming a coating 50 on said core, and an electricall conducting sleeve member surrounding the element, said sleeve being in the form of a logarithmic horn having its throat portion in contact with one end of the resistance element and forming the return conductor for the said end of the resistance element.

3. An electrical resistor comprising an insulating core, a resistance element forming a coating on said core and a sleeve member of electrical resistance material surrounding the element, said sleeve having one end connected to an adjacent end of the resistance element.

4. An electrical resistor comprising a central resistance element and an electrically conducting sleeve surrounding the element and short circuited therewith at one end, the relationship between the characteristic impedance 2 at a point at a distance 2: along the element from the short circuitandmtheresistanceperunitlengthofthe element being givenby m 5. An electrical resistor comprising a central resistance element and a'sleeve member of electrical' resistance material surrounding the element, said sleeve being in the form of a logarith- 10 mic horn and having the throat portion thereof connected to an adjacent end of the resistance element.

6. An electrical resistor comprising a central resistance element and an electrically conducting g sleeve member surrounding the element, said the flared end of metal sleeve II. In instances requiring that a resistor be connected to a consleeve being in the form of a logarithmic horn having its throat ortion connected to one end of the resistance element and forming the return conductor for the said end of the resistance '0 element.

'1. A termination impedance for an ultra-high frequency communication system consisting of two concentric elements, one element being tubular and supporting a conducting shell to constitute 5 a resistance element; and the second element be- 1 ing of electrically conducting material and encircling the tubular element short-circuited to one end of the conducting shell, the diameter of the inner surface of the encircling element in a so plane transverse to the inner element being equal to z Des -K as where D is the outer diameter of the conducting 40 of the ratio of the maximum diameter of the encircling element to the diameter of the tubular shell.

8. A termination impedance as described in" claim 7 in which the tubular element includes an 4 energy-transfer medium to aid the conducting resistance shell to dissipate a substantial quantity of energy supplied from the system.

9. A termination impedance for an ultra-high frequency system, comprising an insulating tubular corej a resistance element forming a coating on said core: and an electrically conducting sleeve member concentrically surrounding the resistance element, said sleeve being in the form of a logarithmic horn having its throat portion in 65 short-circuit contact with one end of the resistance element and forming the return conductor for that end of the resistance element, the logarithmic form of the horn following the equation a=D,.%K where d is the varying diameter of the horn, D1

is the outer diameter of the resistance element, and l is its length, a: is the independent variable 65 representing the distance along the resistance, 

